Show that is divisible by 7 where n is a positive integer. How do I do this question? I solved it by just showing like
which equals to 14 and is divisible by 7
which equals to 28 and is divisible by 7
hence, proven.
But is it correct to show it just like that?
Hey...let's get back to the real question. In other words, I don't really get what flyingsquirrel is trying to say because he ends up with another question. I just wanted to know if my solution above in the description of my question is correct or not because as flyingsquirrel said, I was just showing that 7 divide by is true for n = 1 and n = 2.
Can my solution be accepted by examiners?
I would kindly prefer just a simple yes if my solution is right and if my solution is wrong, please do kindly explain...remember to include yes or no! Thanks.
You only showed that it is true for n = 1 and n = 2. You did not show it to be true for all positive integers. So in short, your solution is not complete.
Pay attention to flyingsquirrel's and mrfantastic's hints and use it to factor the general expression.
I don't think anyone has mentioned it yet but a proof by induction works pretty well.
Firstly, as you have shown, it is true for n=1.
Assume true for n=k:
For n=k+1:
and using Mr Fantastic's factorisation: which is divisible by 7 by our induction hypothesis.
(alternatively which is divisible by 7).
Hence it's true .